Uniqueness of Kusuoka Representations
AbstractThis paper addresses law invariant coherent risk measures and their Kusuoka representations. By elaborating the existence of a minimal representation we show that every Kusuoka representation can be reduced to its minimal representation. Uniqueness -- in a sense specified in the paper -- of the risk measure's Kusuoka representation is derived from this initial result. Further, stochastic order relations are employed to identify the minimal Kusuoka representation. It is shown that measures in the minimal representation are extremal with respect to the order relations. The tools are finally employed to provide the minimal representation for important practical examples. Although the Kusuoka representation is usually given only for nonatomic probability spaces, this presentation closes the gap to spaces with atoms.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1210.7257.
Date of creation: Oct 2012
Date of revision: Feb 2013
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